Band structures, optical selection rules and magnetic dipole moments of topological excitons in flat-band Chern insulators

Exciton bound states in a flat-band Chern insulator are determined by the quantum geometry and topology of the Bloch wave functions of electrons. We numerically solve the exciton Wannier equations for two-dimensional flat-band tight-binding models, taking into account the effective long-range Coulomb interaction. For the center-of-mass (COM) at rest, we determine the nonhydrogenic spectra, profile-function topologies, effective electric dipole moments as well as optical selection rules of the exciton bound states. For the COM motion, we calculate the exciton band structures and obtain the effective masses and anomalous velocities. Moreover, we obtain the exciton magnetic dipole moments inherited from the Bloch bands.